Question

k=550 St=500 r=2.5%\sigma=0.25 u=1.20 d=0.83 q=2.36. K is strike price, St is share price at current time, r is interest,\sigmais volatility and q is the probability path. Work out the branches of this 2-step binomial tree and calculate the possible share prices at T=6 months and then compute the expected share price at T=6 months. Use St as the starting price. Use risk-neutral probabilities to calculate the risk-neutral expected payoff of your Put Option and compute.

Answer 1

The expected share prices at T=6 months using a two-step binomial tree are computed by multiplying the current share price with up and down factors, then using risk-neutral probabilities and discounting to compute the Put Option payoff.

Step-by-step explanation:

To calculate the possible share prices at T=6 months using a two-step binomial tree, you start with the current share price (St), then multiply by up (u) and down (d) factors in each step. The two-step model will show four possible prices at T=6 months:
- St × u × u
- St × u × d
- St × d × u
- St × d × d
For the expected share price at T=6 months, you calculate the risk-neutral probabilities, p = (e^rt - d) / (u - d), and 1-p for the down move, and weight these probabilities to calculate the expected stock price at T=6 months. Finally, use these probabilities to calculate the risk-neutral expected payoff for a Put Option using the formula: Payoff = max(K-S, 0) discounted back to present value using the risk-free rate r.